If x 1, then (2cx^2 + 4cx + cy)/c(x + 1 )^2 =

Question

If x ≠ –1, then  \frac{2cx^2 + 4cx + cy}{c(x + 1 )^2} =

(1) y = 2
(2) c = 3

Shishou · Answer

2cx2+4cx+cy/c(x+1)^2 can be factorised by bringing the c out in the denominator and numerator. This leaves us with 2x2+4x+y/(x+1)^2. 
Statement I says y=2 . This makes the numerator 2x^2+4x+2. The denomiantor when multiplied out is x^2+2x+1 which is half of the numerator. Sufficient

Statement II just gives us the value of c which is not enough.

ANswer is A

Kinshook · Answer

If x ≠ –1, then 
 \frac{2cx^2 + 4cx + cy}{c(x + 1 )^2} = \frac{2(x+1)^2 + (y-2)}{(x+1)^2} = 2 + \frac{(y-2)}{(x+1)^2}

(1) y = 2
 \frac{2cx^2 + 4cx + cy}{c(x + 1 )^2}= 2 + \frac{(y-2)}{(x+1)^2} = 2 
But if C=0, the expression is not valid.
NOT SUFFICIENT

(2) c = 3
Expression is not dependent on C
But we have to make sure that C is not 0.
NOT SUFFICIENT

Combining (1) & (2)
(1) y = 2
(2) c = 3
If c=3, c<>0 
and y=2
 \frac{2cx^2 + 4cx + cy}{c(x + 1 )^2}= 2 + \frac{(y-2)}{(x+1)^2} = 2

IMO C

gvij2017 · Answer

Can I cross off a variable as you crossed off "C" from numerator and denominator. What if value of C is 0. 
If it is mentioned that C is not equal to zero, then I can cross off the C from both side or from numerator and denominator. 
From above thought, I think option C is correct here.

Kinshook · Answer

Yes
I think you have a valid point.
Corrected.

eakabuah · Answer

If x is not equal to -1 then (2cx^2+4cx+cy)/(c(x+1)^2) =?

1. y=2;
This reduces the expression to (2cx^2+4cx+2c)/(c(x+1)^2)
= (2c(x^2+2x+1))/(c(x+1)^2)
= (2c(x+1)^2)/(c(x+1)^2)
Since we know from the question that x is not equal to -1, the above expression results in a value of 2 for values of c not equal to 0. However when c=0, the expression is undefined. But there is no restriction on the value c such that c is not equal to 0, hence statement 1 is not sufficient on its own.

2. c=3 leads to 
(6x^2+12x+3y)/(c(x+1)^2)
When y=2 and x=1, (6(1^2)+12(1)+3(2))/(3(2^2))
=(24)/(12)=2
When y=1 and x=1,
(6*1^2+12*1+3*1)/(3(2^2))
=21/12 =7/4 and this is different from the previous value of 2. Statement 2 is not sufficient.

Combining 1 and 2 yields (2*3(x+1)^2)/(3(x+1)^2) = 2 for all values of x not equal to-1. Hence 1+2 is sufficient.

Answer is therefore C.

Posted from my mobile device

Kinshook · Answer

Firstly, I solved the problem and found A as an answer. 
Then a reply made stated that c should not be zero for results to be valid. 
Then I relooked my solution and confirmed that statement 2 provides that c is not zero and is essential to the solution. 
I revised my solution and put C as an answer.
But now OA is A.

Please correct.

If x 1, then (2cx^2 + 4cx + cy)/c(x + 1 )^2 =

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